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MAA AMC
AMC 12/AHSME
1995 AMC 12/AHSME
11
Three conditions and number
Three conditions and number
Source:
November 21, 2005
Problem Statement
How many base 10 four-digit numbers,
N
=
a
‾
b
‾
c
‾
d
‾
N = \underline{a} \underline{b} \underline{c} \underline{d}
N
=
a
b
c
d
, satisfy all three of the following conditions?(i)
4
,
000
≤
N
<
6
,
000
;
4,000 \leq N < 6,000;
4
,
000
≤
N
<
6
,
000
;
(ii)
N
N
N
is a multiple of 5; (iii)
3
≤
b
<
c
≤
6
3 \leq b < c \leq 6
3
≤
b
<
c
≤
6
.
(
A
)
10
(
B
)
18
(
C
)
24
(
D
)
36
(
E
)
48
\mathbf{(A)}\; 10\qquad \mathbf{(B)}\; 18\qquad \mathbf{(C)}\; 24\qquad \mathbf{(D)}\; 36\qquad \mathbf{(E)}\; 48
(
A
)
10
(
B
)
18
(
C
)
24
(
D
)
36
(
E
)
48
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